DE VARIIS LATINIS GRAECISQVE COLLOQVENDI FORMVLIS ENCHIRIDION IN ANGLICAM LINGVAM CONVERSIS ΠΕΡΙ ΠΟΙΚΙΛΩΝ ΡΩΜΑΙΚΩΝ ΤΕ ΚΑΙ ΕΛΛΗΝΙΚΩΝ ΤΗΣ ΟΜΙΛΙΑΣ ΡΗΤΡΩΝ ΕΝΧΕΙΡΙΔΙΟΝ ΕΙΣ ΤΗΝ ΑΝΓΛΙΚΗΝ ΓΛΩΤΤΑΝ ΜΕΘΕ...
DE VARIIS LATINIS GRAECISQVE COLLOQVENDI FORMVLIS ENCHIRIDION IN ANGLICAM LINGVAM CONVERSIS ΠΕΡΙ ΠΟΙΚΙΛΩΝ ΡΩΜΑΙΚΩΝ ΤΕ ΚΑΙ ΕΛΛΗΝΙΚΩΝ ΤΗΣ ΟΜΙΛΙΑΣ ΡΗΤΡΩΝ ΕΝΧΕΙΡΙΔΙΟΝ ΕΙΣ ΤΗΝ ΑΝΓΛΙΚΗΝ ΓΛΩΤΤΑΝ ΜΕΘΕ...Full description
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Corporate Finance and Portfolio management 1. Net Present Value NPV CF0 Invest if : NPV > 0
CF1 (1 r)
2. Internal Rate of Return
CFt
(1 IRR) t 0
t
Invest if: PI > 1.0
(1 r)
CFn
......
2
(1 r) n
0
Do not invest if: IRR< r
3. Average Accounting Accounting Rate of of Return (AAR)=
4. Profitability Index PI=
CF2
Do not invest if: NPV< 0 n
Invest if: IRR > r
1
Average net income Average book value value
PV of future cash flows Initial Invesments
1
NPV Initial Invesment
Do not invest if: PI< 1.0
5. Cost of Capital (WACC) w d r d (1 t) w p r p
w e r e
where wd = target debt proportion in total capital rd = the before-tax marginal tax rate
t = the company’s marginal tax rate
wp = target preferred stock proportion in total capital rp = the marginal cost of preferred stock
re = the marginal cost of equity
we = target common stock proportion in total capital
E(R i ) R F β i ER M R F 6. Capital Asses Pricing Model Approach E(R where β I = the return correlation of stock i to changes in the market return E(RM) = the expected return on the market
7. Dividend Discount Model Approach V0 = where V0 = the intrinsic value of a share re = the cost of equity 8. P 0 9.
Annualized standard deviation of equity index 11. Country equity premium= Sovereign yield spread Annualized standard devation of the soverign bond market in terms of the development market currency
12. The cost of preferred stock is the preferred stock dividend divided by the current preferred stock price :
r p
D p P p
13. We can estimate the growth rate in the dividend discount model by using published forecasts of analysts or by the s ustainable growth rate:
D ROE EPS
g 1
14. Current Ratio =
15. Quick Ratio =
Current as sests Current liabilities
Cash Short-ter m marketable invesme nts Re ceivables
18. Number of days of receivables = 19. No. of days of inventory =
Accounts r eceiveable Average da y's sales on credit
Inventory Average da y's cos t of goods sold
=
=
Accounts r eceivable Sales on c redit / 365
Inventory Cost of goods sold / 365
20. Operating cycle = Number of days of inventory + Number of days of receivables 21. Net operating cycle = Number of days of inventory + Number of days of receivables - Number of days of payables
Face value - Purchase price 360 Purchase price Number of days to maturity Face value - Purchase price 365 23. Bond Market yield = Purchase price Number of days to maturity 360 Face value - Purchase price 24. Discount- basis yield = Face value Number of days to maturity 22. Money Market yield =
25. Cost of trade credit = 1
Discount 1 Discount
365 Number of days beyon d discount period
Net income 26. Return on equity =
Average shareholders' equity Revenues Average total assets
27. Standard Deviation = σ
2
1
Net income Revenues
Average total assets
Average shareholders' equity
n
[R E(R )] i
i
2
Pi
i 1
28. rij=
Covij i j
where rij= the correlation coefficient of returns i = the standard deviation of R it
29. po rt
j
= the standard deviation of R jt
w12 12 w22 22 2w1 w 2 r 1, 2 1 2 Derivatives and Alternative Investments
1. FRA payoff formula (from the perspective of the party going )
Days in underlying rate Underliying rate at expiration Forward contract rate 360 Notional Principal = Days in underlying rate 1 Underlying rate ate xpriation 360 2. Minimum and Maximum Values of Options Option European call
4. (Shareholders’ equity)- (Total value of equity claims that are senior to common stock) = Common shareholders’ equity
5. (Common shareholders’ equity)/ (Number of common stock shares outstanding) = Book value per share
Price = Par value Coupon rate < Yield required by market Price < Par value (discount) Coupon rate > Yield required by market Price > Par value (premium)
6. Coupon rate = Yield required by market
7. Price of callable bond = Price of option-free bond – Price of embedded call option 8. Price of putable bond = Price of option- free bond + P rice of embedded put option 9. Taxable-equivalent yield =
Tax exempt yield 1 - Marginal tax rate
1 1 1 i no .of period s 10. Present value of an annuity = Annuity payment i 11. Valuing a Zero- Coupon Bond
Maturity v alue 1 i no. o f years 2
Where i is the semiannual discount rate
12. Current yield =
Annual dollar coupan interest Price
Yield on a bond - equivalent basis 2 13. Yield on an annual-pay basis 1 1 2 14. Spread for life =
Net income - Preferred dividends Weighted average number of shares outstanding
Net income After tax int rest on convertibl e debt Pr eferred di vidends 3. Diluted EPS = Weighted a verage num ber of sha res
outs tan ding New common shares that could have been issu ed at conv ersion
4. Diluted EPS =
Netincome Preferred dividends Weighted average number of shares outstanding New shares that could have been issued at option excersice Shares that could have been purchased with cash received upon excersice
5. Net profit margin =
Net income
6. Gross profit margin=
Revenue
Gross profit Revenue
7. FCFF= NI + NCC + Int (1-Tax rate)- FCInv – WCInv 8. FCFF = CFO + Int (1-Tax rate) - FCInv 9. FCFF = CFO- FCInv + Net borrowing – Net debt repayment 10. Definitions of commonly Used Activity Ratios Activity Ratios Inventory Turnover Days of inventory on hand (DOH) Receivables turnover Days of sales outstanding(DSO) Payables turnover Number of days payables Working capital turnover Fixed asset turnover Total asset turnover
Numerator Cost of goods sold Number of days in period Revenue Number of days in period Purchases Number of days in period Revenue Revenue Revenue
Denominator Average inventory Inventory turnover Average receivables Receivables turnover Average trade payables Payables turnover Average working capital Average net fixed assets Average total assets
11. Definitions of commonly Used Liquidity Ratios Liquidity Ratios Numerator Current assets Current ratio Cash + Short-term marketable investments + Receivables Quick ratio Cash + Short-term marketable investments Cash ratio Cash + Short-term marketable investments + Receivables Defensive interval ratio Additional Liquidity Measures Cash Conversion cycle (net DOH + DSO – Number of days of payables operating cycle)
Denominator Current liabilities Current liabilities Current liabilities Daily cash expenditures
12. Definitions of commonly Used Solvency Ratios Solvency Ratios Debt Ratios a Debt-to-assets ratio Debt-to-capital ratio Debt-to-equity ratio Financial leverage ratio Coverage Ratios Interest coverage Fixed charge coverage
Numerator b
Denominator
Total debt b Total debt b Total debt Average total assets
Total assets b Total debt + Total shareholders’ equity Total shareholders’ equity Average total equity
13. Definitions of commonly Used Profitability Ratios Profitability Ratios 10 Return on Sales Gross profit margin Operating profit margin Pretax margin Net profit Income Return on Investment Operating ROA ROA Return on total capital ROE Return on common equity
Numerator
Denominator
Gross profit 11 Operating income EBT (earnings before tax but after interest) Net Income
Revenue Revenue Revenue Revenue
Operating income Net income EBIT Net income Net income-preferred dividends
Average total assets Average total assets Short and long -term debt and equity Average total equity Average common equity
14. ROE = Net profit margin * Asset turnover * leverage 15. ROE = Tax burden * Interest burden * EBIT margin * Asset turnover * Leverage Quantitative analysis 1. Population Mean: calculated as X
1
N
X
i
N i 1
Where there are N members in the population and each observation is Xi i =1, 2, …N. Sum of all the deviations is zero.
2. Sample Mean: calculated as X
3. Weighted Mean: calculated as
1 n
n
X i
i 1
X weighted
n
w X i
i
i 1
4. Geometric Mean: calculated as G
n X 1 X 2 X 3 ... X n
Where there are n observations and each observation is Xi.
5. Mean Absolute Deviation: is the average of the data’s absolute deviations from the m ean.
MAD
1
n
n
X X i
i 1
6. Population Variance: is the average of the population’s squared deviations from the mean.
2
1
N
X N
2
i
i 1
The population standard deviation is simply the square root of the population variance.
7. Sample Variance: is the average of the sample data’s squared deviations from the sample mean. The sample standard deviation is
s 2
1
n
X X n 1
2
i
i 1
8. Covariance describes the co-movement between 2 random numbers, given as : Cov(X1, X2) = σ12
Cov( X , Y ) E [( X X )(Y Y )] Cov( X , Y ) E ( XY ) X Y 9. Correlation coefficient is a unit-less number, which gives a measure of linear dependence between two random variables. ρ(X1, X2) = Cov(X1, X2) / σ1σ2
10. Portfolio Expected Return: E(rp) = wA rA + (1-wA )rB Portfolio Variance: 2 r p OR
w A2 A2 1 w A 2 B2 2w A 1 w A Covr A , r B 2
r
p
11. Coefficient of variation
12. Sharpe measure
SM
w A2 A2 1 w A 2 B2 2w A 1 w A AB A B CV
s X
( r p r f ) p
13. Addition Rule Used to Get Compound Probabilities for Union of Events: P(A OR B) = P(A U B) = P(A) + P(B) - P(A ∩ B) For Mutually Exclusive Events: P(A OR B) = P(A U B) = P(A) + P(B) 14. Sum Rule & Bayes’ Theorem
P ( B) P ( A B) P ( Ac B) P ( B / A) P ( A) P ( B / Ac ) P ( Ac ) P ( A / B)
P ( B / A) P ( A) P ( B / A) P ( A) P ( B / Ac ) P ( Ac )
Out of a group of 100 patients being tre ated for chronic back trouble, 25% are chosen at random to receive a new, experimental treatment as opposed to the more usual muscle relaxant-based therapy which the remaining patients receive. Preliminary studies suggest that the probability of a cure with the standard treatment is 0.3, while the probability of a cure from the new treatment is 0.6.
15. Discrete Probability Distributions Probability distribution for a Binomial random variable is given by: P ( X x )nC p x (1 p )n x x
16. Normal Distribution Random Variable 2
General Normal random variable X ~ N (μ, σ ) X can be standardized to a Standard Normal random variable. Resulting variable has mean zero and variance equal to 1.
Z
X
17. Confidence Intervals
The standard error of the mean (s x) is given by: s x
s n
18. Errors in Estimation Type I and Type II Errors Type I error occurs if the null hypothesis is rejected when it is true Type II error occurs if the null hypothesis is not rejected when it is false Significance Level -> Significance level
The upper-bound probability of a Type I error 1 - ->confidence level The complement of significance level
19. The sample variance for a pooled estimater is given as s 2 20. Hypothesis Tests for Variances